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Multiscale method with model reduction
Fri, 2010-04-16 03:45 - Julien Yvonnet
Model reduction based on Propper Orthogonal decomposition is widely used in Computational mechanics to reduce the number of degrees of freedom in systems. In the attached papers, we introduced a POD-based model reduction in a multiscale framework to significantly reduce the computations.
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[12] R3M.pdf | 1.75 MB |
[17] R3M thermique.pdf | 727.22 KB |
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Very interesting work
Hi Julien,
I am working on homogenization-based multiscale modelling of failure in the spirit of the FE2 method. It is extremely computationally demanding particularly without parallel computers.
I therefore seek for advanced methods to reduce the computational cost and it seems that model reduction might be a good choice. I do not understand your paper fully, but I think model reduction was applied to the micro models. Is this right? Could you tell me to what extent this is independent of the model used at the microscale? For example can it be applied for a continuum damage model at the microscale?
Looking forward to hear from you.
Merci beaucoup.
Dear Vinh
Dear Vinh Phu,
You
are right, in the proposed approach the model reduction is applied to
the local scale. You first need to construct a reduced basis that can
describe your microscale model for different possible loadings
prescribed by the macroscale. In our cases the problems were
history-independent. To my opinion the proposed framework needs to be
extended to be applied to damage model. Model reduction of problems with internal variables has been recently proposed in
Hyper-reduction of mechanical models involving internal variables
Ryckelynck D, International journal for Numerical Methods in Engineering, 77(1): 75-89 (2009).
Maybe there is a hint here to combine multiscale and model reduction for your problems ?
Best regards,
Julien
Hi Julien, Thanks for
Hi Julien,
Thanks for mentioning the paper.
Phu